5.1 Valence Bond Theory | Chemistry: Atoms First 2e

Learning Objectives

Describe the formation of covalent bonds in terms of atomic orbital overlap
Define and give examples of sigma and pi bonds
Calculate bond dipole moments and percent ionic character

Core Concepts & Principles

While VSEPR theory predicts three-dimensional molecular shapes, it does not explain how chemical bonds actually form. Valence bond theory bridges this gap by describing covalent bonds through the quantum mechanical concept of atomic orbital overlap.

Valence Bond & Orbital Overlap Principles

A covalent bond forms when a half-filled atomic orbital on one atom overlaps with a half-filled atomic orbital on another atom, sharing a pair of electrons.
The strength of a covalent bond depends directly on the extent of orbital overlap; greater overlap yields a stronger, more stable bond.
Bond distance (length) represents the optimum distance where attractive forces (nucleus-electron) and repulsive forces (nucleus-nucleus, electron-electron) balance to achieve the lowest possible potential energy.

Types of Covalent Bonds: Sigma and Pi Bonds

Bonds are classified based on how their orbitals overlap along the internuclear axis (the straight line connecting two bonded nuclei):

Sigma bonds ( $\sigma$ bonds): Formed when orbital electron density is concentrated directly along the internuclear axis. These are formed by end-to-end overlap of two $s$ orbitals, an $s$ and a $p$ orbital, or two $p$ orbitals. All single bonds are sigma bonds.
Pi bonds ( $\pi$ bonds): Formed by the side-by-side overlap of two parallel $p$ $p$ orbitals. The regions of electron density lie on opposite sides of the internuclear axis. Directly along the axis itself lies a node—a plane with zero probability of finding an electron.
- Multiple bonds: A double bond consists of 1 $\sigma$ bond and 1 $\pi$ bond. A triple bond consists of 1 $\sigma$ bond and 2 $\pi$ bonds. Between any two atoms, the first bond formed is always a $\sigma$ bond.

Coulombic Forces and Dipole Moments

Real bonds frequently fall between pure covalent and pure ionic. Coulomb's law describes the electrostatic attraction between charged particles:

Coulombic Force ( $F$ ):

F = \frac{Q_1 Q_2}{d^2}

Potential Energy ( $E$ ):

E = \frac{Q_1 Q_2}{d}

When charges are permanently concentrated more on one atom than another in a covalent framework, the molecule is polar and possesses a bond dipole moment ( $\mu$ ), measured in Debyes (D). Comparing experimental dipole moments to theoretical 100% ionic models reveals a bond's partial ionic character.

Problem-Solving Routines & Methods

Bond Dipole Moment Formula

\mu = Q \cdot d

Calculates the dipole moment of a diatomic molecule.

Variables & Constants

Q

=charge magnitude (C);

d

=bond distance (m);

\mu

=dipole moment

Percent Ionic Character Formula

\text{Percent Ionic Character} = \left(\frac{\mu_{\text{exp}}}{\mu_{\text{lim}}}\right) \times 100\%

Determines the ionic percentage of a polar covalent bond.

Variables & Constants

\mu_{\text{exp}}

=experimentally measured dipole moment;

\mu_{\text{lim}}

=calculated limiting dipole moment for a purely ionic bond

How to Calculate Percent Ionic Character

1
Calculate the theoretical limiting dipole moment ( $mu_{\text{lim}}$ ) by multiplying the elementary electron charge ( $1.602 \times 10^{-19}\text{ C}$ ) by the bond length in meters.
2
Convert the resulting charge-distance product from $ext{C}cdot\text{m}$ to Debyes by dividing by $3.336 \times 10^{-30}\text{ C}cdot\text{m/D}$ .
3
Divide the experimental dipole moment ( $mu_{\text{exp}}$ ) by this limiting value and multiply by 100.

Pro-Tip: Always convert bond lengths given in picometers (pm) or nanometers (nm) into meters (m) before performing calculations.

Practice & Concept Checks

Concept Check

What distinguishes a sigma bond from a pi bond in terms of electron density and nodal planes?

Concept Check

Why does a double bond consist of one sigma bond and one pi bond rather than two sigma bonds?

Key Terms & Vocabulary

Valence bond theoryBonding Theory

A model that describes a covalent bond as the overlap of half-filled atomic orbitals, resulting in a pair of shared electrons between bonded nuclei.

Example: Explains bonding in diatomic molecules like H₂ and HCl.

overlapQuantum Mechanics

The condition where a portion of an atomic orbital from one atom and a portion of an orbital from another atom occupy the same region of space.

Example: Greater orbital overlap produces stronger, more stable covalent bonds.

sigma bonds (σ bonds)Bond Types

Covalent bonds formed when electron density is concentrated along the internuclear axis via end-to-end orbital overlap.

Example: All single covalent bonds are sigma bonds (e.g., s-s, s-p, or end-to-end p-p overlap).

pi bond (π bond)Bond Types

A covalent bond formed by the side-by-side overlap of parallel p orbitals, with regions of electron density residing on opposite sides of the internuclear axis.

Example: Present in double (1

\sigma

, 1

\pi

) and triple (1

\sigma

, 2

\pi

) bonds.

nodeQuantum Mechanics

A plane or spatial region along the internuclear axis of a pi bond where the probability of finding an electron is exactly zero.

Example: Located in the nodal plane directly between bonded atoms in a pi bond.